The topological nature of axion couplings to gauge bosons offers unique opportunities to obtain information about the UV limit of the SM. The coupling to photons is particularly important experimentally. I will discuss why the discovery of an axion-like particle above the QCD line would rule out 4d grand unified theories, the perturbative heterotic string, and F-theory GUTs. 

Based on 2206.07053, 2410.03820 and 2509.08042 + ongoing work.